#### Henri Poincaré, The logic of infinity: The cardinal number

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We must not forget the preceding considerations when defining the cardinal number. If we consider two collections, we may seek to establish a law of correspondence between the objects of these two collections, so that any object of the first … Read More

#### Henri Poincaré, The logic of infinity: What a classification must be

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Can the ordinary rules of logic be applied without change, as soon as we consider collections taking an infinite number of objects? This is a question we did not ask at first, but we were led to examine when the … Read More

#### Henri Poincaré, Why space with three dimensions – Analysis Situs and intuition

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I would like to add a remark which relates only indirectly to the foregoing; we have seen above the importance of the Analysis Situs and I explained that this is the real domain of geometric intuition. Does this intuition exist? … Read More

#### Henri Poincaré, Why space with three dimensions – Space and Nature

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But the question can be asked from a completely different point of view. We have so far placed ourselves in a purely subjective, purely psychological or, if you will, physiological point of view; we have only considered the relations of … Read More

#### Henri Poincaré, Why space with three dimensions – Space and movements

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It seems, therefore, that space cannot be constructed by considering sets of simultaneous sensations, which must be considered as sequences of sensations. Always go back to what I said before. Why do certain changes appear to us as changes of … Read More

#### Henri Poincaré, Why space with three dimensions – Space and senses

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The question seems resolved; we seem to have only to apply this rule, either to the physical continuum, which is the coarse image of space, or to the corresponding mathematical continuum which is its refined image and which is the … Read More

#### Henri Poincaré, Why space with three dimensions – Continuum and cuts

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But what is a continuum with n dimensions; how does it differ from a continuum whose number of dimensions is larger or smaller? First, let us recall some results recently obtained by the students of Cantor. It is possible to … Read More

#### Henri Poincaré, Why space with three dimensions – Analysis Situs (Topology)

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Geometers usually distinguish two kinds of geometries, which they call the first of metric and the second of projective; metric geometry is based on the notion of distance; two figures are regarded as equivalent when they are “equal” in the … Read More

#### Henri Poincaré, Space and time (1)

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One of the reasons that led me to return to one of the questions I have most often dealt with, is the recent revolution in our ideas on mechanics. Will the principle of relativity, as conceived by Lorentz, not impose … Read More

#### Henri Poincaré, The evolution of laws (11)

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So far we have not seemed to worry about whether laws actually vary, but only if men can believe them to be variable. Are laws considered to exist outside the mind that creates or observes them immutable in themselves? Not … Read More

#### Henri Poincaré, The evolution of laws (10)

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Thus there is not a single law that we can state with the certainty that it has always been true in the past with the same approximation as today, I will say more, with the certainty that we will never … Read More

#### Henri Poincaré, The evolution of laws (9)

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Let us return to our imaginary world and ask ourselves if its inhabitants could not, without renewing the history of the sleepers of Ephesus, perceive this evolution. No doubt, no matter how perfect the heat conductivity on their planet, it … Read More